Generating Special Curves for Cubic Polynomials - Khudoyor Mamayusupov; Figen Çilingir; Marks Ruziboev; Gafurjan Ibragimov; Bruno Antonio Pansera (Mathematics)
An algorithmic method is proposed to generate all cubic polynomials with a critical orbit relation. We generate curves (polynomials of parameters) that correspond to those functions with critical orbit relations. The irreducibility of the polynomials obtained is left as an open problem. Our approach also works to generate critical orbit relations in all families of rational functions with active critical points.